In this paper, two new efficient detection algorithms, Type 1 (T1) with better complexity-performance tradeoff and Type 2 (T2) with lower complexity, are derived from one generalized framework for multiple-input multiple-output (MIMO) communication systems. The proposed generalized detection framework constructed by parallel interference cancellation (PIC), group, and iteration techniques provides three parameters and three sub-algorithms to generate two efficient detection algorithms and conventional BLAST-ordered decision feedback (BODF), grouped, iterative, and B-Chase detection algorithms. Since the group interference suppression (GIS) technique is applied to the proposed detection algorithms, the complexities of the preprocessing (PP) and tree search (TS) can be reduced. In (8,8) system with uncoded 16-QAM inputs, one example of the T1 algorithm can save complexity by 21.2% at the penalty of 0.6 dB loss compared with the B-Chase detector. The T2 algorithm not only reduces complexity by 21.9% but also outperforms the BODF algorithm by 3.1 dB.